Petr Polák was driving through his home town in the Czech Republic when he noticed something unusual about the journey. He recalls: “All of a sudden there were stairs on the road so the car was bumping along them. It was strange and I knew there was something wrong. So I looked at my hands and I had an extra finger on one of them. I thought, ‘Wow, this is a dream.’ But I was so excited that I woke up seconds later.”

It was the first time that the owner of coffee house Maryčka, based in the Czech city of Ostrava, had experienced a phenomenon called lucid dreaming, an elusive state in which you consciously know you are dreaming. Unlike a regular dream where there is no control over what you experience, a lucid dream offers you the possibility to influence your surroundings and choose which activities to engage in. It is like virtual reality, but within your own head. But are dreams really an effective space for entrepreneurs to problem solve, generate new ideas and even learn new skills?

Daniel Erlacher, a neuroscientist at the University of Bern, Switzerland, believes they can be. He explains that because the brain is in a less rational “free association state” the dream is the perfect environment for creative thinking. In a joint study with colleagues at the University of Heidelberg in 2012, Erlacher found that while most lucid dreamers participating in the research used the experience to have fun, 29% used it for problem-solving, 27% explored creative ideas and insights and 21% practised skills.

Polák is eager to learn how to prolong his experience of lucid dreaming so is experimenting with different techniques to induce the experience. He wants to use his moments of nighttime lucidity to improve his business. And that is not as unlikely as it sounds.

A study at the University of Lincoln in 2014 found that people with frequent lucid dreams are better at cognitive tasks performed while awake that involve insight, such as problem-solving.

US-based entrepreneur Jody Clower says she regularly brainstorms in her lucid dreams and that she came up with the name for her property tech startup Nestiny during one experience.

She says: “I like portmanteaus, so I had ideas floating around my head and, for about a week or so, I tried to come up with something. I liked the word nest because it had an implied meaning of cosiness and home, but I just couldn’t find the right thing to go with it. Then one night I was in a lucid dream and it occurred to me to put the word nest together with the word destiny. It made sense and I woke up thinking ‘That’s it!’”

Using lucid dreaming to solve problems is not without challenges, however. Lucid dreams can be frustratingly brief, Clower says. “Every now and then, I will hit a brick wall when brainstorming, mostly solutions too intricate or complex work problems … Those can be a bit frustrating because I am racing during the dream to arrive at a solution because I know that the time is precious.”

With many small business owners already struggling to get a good night’s sleep, some may be concerned that being “awake” in their dreams will take a toll on their mental alertness during the day.

According to Stephen LaBerge, psychophysiologist and a leader in the scientific study of lucid dreaming, the experience is usually just as restful as non-lucid dreaming. Indeed, studies by the neuropsychologists Ursula Voss and Martin Dresler have shown that brain activity while lucid dreaming is similar to the regular REM (rapid eye movement) sleep during which we all dream.

However, in his bestselling book Exploring the World of Lucid Dreaming, LaBerge writes that how tired you feel after a dream depends on what you did in the dream. For example, Clower admits that while most mornings she wakes up feeling refreshed, a night of intense problem-solving while lucid dreaming can sometimes mean she is mentally exhausted the next day.

Lucid dreaming can have more than just a psychological effect on practitioners. Erlacher has found that mentally practising an activity during dreams can even improve physical skills. In one small study, published in the journal Sport Psychologist in 2010, lucid dreamers were asked to toss coins into coffee cups before bed and then dream about themselves practising that night. In the morning, when asked to toss coins again, the lucid dreamers who successfully practised while dreaming were more accurate, compared with those who failed to practise and a control group of non-lucid dreamers.

Choreographer Jade Shaw, who founded small business ParkourDance in 2012 after brainstorming the idea during a lucid dream, says she has experienced this first hand. She claims that after practising aerial cartwheels in a dream state she felt it was easier to perfect the movement while awake. Although she admits she couldn’t be sure what level of impact her lucid dream activity really had on her performance.

There are limitations to what entrepreneurs can do in a lucid dream. Erlacher says: “A lucid dream will not help you to learn another language if you have never heard it before. You have to have some experience with the things you practise in your dreams. It’s not a miracle.”

But before small business owners start thinking they have a new, handy way to rehearse an important pitch or come up with an invention, be warned; learning how to get lucid in a dream is not easy, it takes time, effort and a little luck.

Scientists such as LaBerge devised techniques to induce lucid dreams, most notably the Mild technique (mnemonic induction of lucid dreams). This involves improving dream recall – for example, by keeping a dream journal, repeatedly questioning whether you are awake or dreaming, regular affirmations to get lucid and visualisations before sleeping. And a plethora of gadgets are now available claiming to help get users to that state while asleep.

Sadly, Erlacher says that there is no foolproof way to induce lucid dreams. In fact, only about 20% of the population claim to have lucid dreams once a month or more. He says that most people will have to train for one to two months for their first lucid dream using an induction technique.

“If you want to have more lucid dreams you have to continue with your training,” says Erlacher. “That’s the major obstacle in lucid dream research, to find reliable, easy to apply techniques to induce lucid dreams.”

Sign up to become a member of the Guardian Small Business Network here for more advice, insight and best practice direct to your inbox.